hw4-2010

# Hw4-2010 - Binary search trees Greedy algorithms Homework 4 Due Date Tuesday 9 November 2010 2:05pm Problem 4-1 20pts Suppose that a search for key

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Binary search trees, Greedy algorithms October 31, 2010 Homework 4 Due Date: Tuesday, 9 November 2010, 2:05pm Problem 4-1. 20pts Suppose that a search for key k in a binary search tree ends up in a leaf. Consider three sets: A , the keys to the left of the search path; B , the keys on the search path; and C , the keys to the right of the search path. Provide a small counterexample that disproves the following claim: Any three keys a A, b B, c C must satisfy a b c . Problem 4-2. 20pts An alternative method of performing an inorder tree walk of an n -node binary search tree ﬁnds the minimum element in the tree and then ﬁnding its n - 1 successors, one at a time. In other words, if minimum is a , then ﬁrst ﬁnd a , then ﬁnd b =successor of a , then c =successor of b , etc. Prove that this algorithm runs in Θ( n ) time. [Note that one cannot claim that ”successor” operation always takes O (1) time, even for an approximately balanced binary search tree.] Problem 4-3. 25pts
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## This note was uploaded on 02/01/2011 for the course MATH 171 taught by Professor R during the Spring '09 term at Stanford.

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